Tuesday, December 12, 2006

My latest mental wanderings

Consider, if you will, the philosophy of math. Most people will usually start with the point and work their way outward expanding on the logic that came before Inductive reasoning at its finest. I'm going to try the reverse. Imagine if you will a four dimensional object. Any four dimensional object. Ok that didn't work. We'll go slightly smaller to make it somewhat easier. Imagine if you will a three dimensional object, any object in R3 (that's fancy math speak for it has three dimensions). Why was it there? What is it that determines where it exists and for how long?

Some might answer that it is the mathematician that holds the entire fate of this shape in his hands controlling where it is place what its dimensions are where it is defined and the rest of the whole gamut of a 3D objects life. Is this the case, or is it that the shape was always there and the mathematicians have just now discovered it? Was Shroedenger right? Do we need to oberserve something for it to exist or is its existance independant of our observation? Can we reach our full potential on our own or do we need the input of others? Does our work exist if there is no one to recognize it? Or are we dependant upon the imaginations of others in our very existance? Can we determine ourself or are we constructed by society?

Let us consider this shape further. Regardless of the details a shape exists (?). But why does it take the form it does? One answer to this is that it is defined by what came before, a shape is defined by the pieces that make it up. A cube is defined by the square. A sphere is defined by its circle. All of these can be represented by equations once initial parameters have been defined. We are a product of our component parts and we too are subject to what has come before. We are the integration of our genetics, our parent's are friends all of history, all of time and space. We are a product of the equations that compose us DNA RNA et al, and we are of our environment. We are the function that effects and is effected by the vector field. There are forces acting upon us at every point in every second for all time. But here there is a difference between us and the cube. We are non-deterministic. We have free will we are able to choose our path and our actions even though they might be played out for us.

How is this possible you might ask. Consider this, On my calculator I have on my calculator a function composed of three completely random variables. It is impossible for me to predict the path it will take, I do not know how long it will take, but I know without a doubt the final outcome. Always. Even though the function is completly random. I love this program as it is metaphoric of our very existance. Some might say that if we truly have free will how then can an all knowing God know what we will do? Others suggest that if there is no god what then is the point of our existance (to find our very purpose IS our purpose, but this is a subject for a later day!). But if we have a devine plan how can we possibly have free will? The function to which I earlier alluded provides the key. There is an equation that models the path. There is a god over seeing our lives, there is a purpose an equation of life if you will. But there is also free will randomness. The answer is known, and yet it isn't! I suggest as evidence of this, consider God hedging his bets. Inspiring two people simultaneously one accepting one choicing to reject, perhaps even God doesn't know which is which. Perhaps he can see all possible outcomes of either one or both. I do not know. but this would predict, if it were true that many people should be inspired by similar ideas at about the same time. Alexander Graham Bell Patented the telephone 4 hours before a William (?) Grey. Nichola Tessla patented the radio days before Marconi. The pattern repeats throughout history. What does that mean? That is for you to say.
But, we are not done yet. Let us consider again that shape we obtained earlier. It is true that a shape is defined by its component parts, but how we perceive these parts is subject to interpretation. See this post and its link. (check it out later its worth it.)


That shape we were mentioning: what would happen if it were a cylinder? When viewed from the side its component part is a two dimensional rectangle. If you are in a 2D mindset no matter how you look at it, even if you consider all of the evidence available to you, you will only, can only see a 2 dimensional rectangle. If you are in side of this rectangle you will see material in every direction you look. If you are suck viewing this object from above or below you will see something completely contradictory to a rectangle. You will see a circle. Were the viewer of the circle to meet the viewer of the rectangle or the viewer of empty space They would each be solidly convinced (I would apologize for the pun, but its my site so I won't) that what they saw was truly universal truth. It could be no other way. For how on Earth can a circle be a rectangle. You are WRONG I am RIGHT! Universal truth is MINE! GOD is on MY SIDE! Your comment that God is a rectangle--pure lunacy! We shall war!

But wait, they are both right, even though they are contradictory. God is one, God is all. He is within us and around us. We are in his image. He act through us and we become him. God is singular and he is pluaral. He is here and now and there and then. He has a plan and we are part of it yet we are allowed to do our thing. 3-1-300,000 It is all the same. Truth exists for everyone.

Ah, but here's the kicker. We still are not done! We have considered the solid, made mention of the fact there are probably other solids out there possibly even in here. It is only a matter of where you search and being open to the answers you find. Let us complete our mathematical journey and consider my final point (pun intended). The zero dimensional object.

We have said that a shape is determined by is component surfaces--Remembering it is entirely possible to have infinitely many surfaces, a shape is nonetheless determined by them. And that a surface is constrained by the many vectors that make up its existance. But what about a point? Why is a point there? A line exists and is defined if only one other point exists. A rule a guideline. A constraint of society. Others will force us into a fixed mold, but the point is free. The point is Zen. Two points is rules and society. Interaction with others. One point is self and the only thing that can be said of the point is where it is at and that it exists. Our observation affects the point because as soon as we observe it there is a distance between us and it there is a path a destination a line/line segment--a line cut short of its full potential. It is unknown what it could have been or how far along in its life it would have been if we were not there. A point, an individual can become anything go anywhere. More fascinating still is that from just a few points an entire world can be defined. Change even 1 point and the world is a different place. Change even one life and the world is changed.

Remember the individual is free to act. And it is the individual at the intersection of infinitely many others that changes the path the others were traveling. X two lines composed of infinitely many individuals intersect always at only one point. It is up to the dot the zero dimensional object. The things that cannot be measured and are not seen that matter most. They are the ones who can change the line of societies path.

In short, be the dot! Change the worlds path! You can do it! All you have to do is plot out how. Good Night, Good Luck!


Boom said...

And you thought math wasn't interesting.

Incidently if you are interested in the program: Here is how you can graph the Sierpinski triangle on a TI-83.

Incidently comments page doesn't like greater than or less than signs so gt means greater than. lt meas less than gt/et is greater than equal to, lt/et is less than or equal to and an arrow is -)

Program New
Title it (I titled mine:"Sierpins")
:If N gt/et 1/3
:If 1/3 lt N and N gt/et 2/3
:If 2/3 gt N

And that is a program that will graph an object that is the very model of divinity itself. If is an infinite image similar at all scales determined completely at random yet completely predicable. The end is known the path is not. The infinite is contained within the finite. AND you can use the blimey thing to model everything from forest fires, to Zelda logos, and even mountain ranges. Things like that are so why I want to be a math major!

Ki said...

Boom you're a first. Love the flat-lander meets TI. Groovy.

Boom said...

Urm, pardon the technologically inept, but what is a flat-lander, and how did I relate it to my Calculator?